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merge :: (Ord a) => [a] -> [a] -> [a] -- The merge function is a highly-specialized function that merges two infinite, sorted lists
merge xs@(x:xt) ys@(y:yt) =
  case compare x y of
    LT -> x : (merge xt ys)
    EQ -> x : (merge xt yt)
    GT -> y : (merge xs yt)



diff :: (Ord a) => [a] -> [a] -> [a] -- diff, in short, removes all of the elements of the second list passed to it from the first.
diff xs@(x:xt) ys@(y:yt) =
  case compare x y of
    LT -> x : (diff xt ys)
    EQ -> diff xt yt
    GT -> diff xs yt


composites :: [Integer]
composites = foldr1 f $ map g $ tail primes
  where
    f (x:xt) ys = x : (merge xt ys)
    g p = [ n * p | n <- [p, p + 2 ..]]

*Week6> take 10 composites
[9,15,21,25,27,33,35,39,45,49]

Task 6 
Use the list from the previous exercise to test the Miller-Rabin primality check.

The Miller-Rabin test returns 172947529 as prime, but it is a Carmichael pseudo prime. 
To get results with a higher chance to be right, the test should be executed multiple times but with different (random) parameters. 
This was tested with the function checkMillerRabin. It showed that the results are more precise by repeating the test with different random values. 
(This was tested by modifying the functions parameters, not auto-test present yet).

testIntersectionA1 :: Ord a => Set a -> Set a -> Bool
testIntersectionA1 x y = testIntersectionA2 x y (intersection x y)

testIntersectionA2 :: Ord a => Set a -> Set a -> Set a -> Bool
testIntersectionA2 (Set []) y z = True
testIntersectionA2 (Set (x:xs)) y z = inSet x y == inSet x z
&& testIntersectionA2 (Set xs) y z

trClos ::Ord a => Rel a -> Rel a
trClos rel = do trans1 <- return (nub (rel ++ (rel @@ rel)))
                if length trans1 == length rel
                   then rel
                   else trClos trans1